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Block #1,858,333

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/20/2016, 5:53:24 PM Β· Difficulty 10.6760 Β· 4,946,829 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
0ca7eab42fc77365147b5402dcb598f70a9d68f10a6e3a6acdc5afd8f0d7c051
View on Chainz β†—

Height

#1,858,333

Difficulty

10.676047

Transactions

2

Size

1.54 KB

Version

2

Bits

0aad116c

Nonce

2,095,028,145

Timestamp

11/20/2016, 5:53:24 PM

Confirmations

4,946,829

Mined by

⛏️ P2SHAc1GnBDiQ3HX4Tt1PaipZk1q8D6vWL9NZs

Merkle Root

f5bad835f0ceb797d7ac1328d2aea9cc760e5232f12fe44d9e2177a1bfd85fe6
Transactions (2)
Coinbase667d37e7785184…c94fd9d608b7d0
1 in β†’ 1 out8.7800 XPM109 B
Ac1GnBDi…6vWL9NZs
f2cd0d18751250…c5fe91adb10823
9 in β†’ 1 out50000.0000 XPM1.34 KB
AYKArr5V…V9VqiqCZ
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.344 Γ— 10⁹³(94-digit number)
73442785500449948126…39756692267924686219
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
7.344 Γ— 10⁹³(94-digit number)
73442785500449948126…39756692267924686219
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.344 Γ— 10⁹³(94-digit number)
73442785500449948126…39756692267924686221
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.468 Γ— 10⁹⁴(95-digit number)
14688557100089989625…79513384535849372439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.468 Γ— 10⁹⁴(95-digit number)
14688557100089989625…79513384535849372441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.937 Γ— 10⁹⁴(95-digit number)
29377114200179979250…59026769071698744879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.937 Γ— 10⁹⁴(95-digit number)
29377114200179979250…59026769071698744881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
5.875 Γ— 10⁹⁴(95-digit number)
58754228400359958501…18053538143397489759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.875 Γ— 10⁹⁴(95-digit number)
58754228400359958501…18053538143397489761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.175 Γ— 10⁹⁡(96-digit number)
11750845680071991700…36107076286794979519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.175 Γ— 10⁹⁡(96-digit number)
11750845680071991700…36107076286794979521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,685,363 XPMΒ·at block #6,805,161 Β· updates every 60s
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